Can anyone explain both and help me with the answer as well? Thank you!

Suppose you have $13,000 to invest, which of the two rates would yield a larger amount in 1 year: 11% compounded daily or 10.86% compounded continuously
&
As x=-infinity, f(x)=?

11% compounded daily

Step-by-step explanation:

Simple interest is:

A = P (1 + r/n)^(nt)

where A is the final amount,

P is the initial amount,

r is the annual rate,

n is the number of compoundings per year (in this case, 365),

and t is the number of years.

A = 13,000 (1 + 0.11/365)^(365×1)

A = 14,511.37

Continuously compounded interest is:

A = Pe^(rt)

A = 13,000 e^(0.1086×1)

A = 14,491.31

11% compounded daily would yield a larger amount in 1 year.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $13,000

r = 11% = 11/100 = 0.11

n = 365 because it was compounded 365 times in a year.

t = 1 year

Therefore,

A = 13000(1 + 0.11/365)^365 × 1

A = 13000(1 + 0.0003)^365

A = 13000(1.0003)^365

A = $14504.1

The formula for continuously compounded interest is

A = P x e(r x t)

From the information given,

P = $13000

r = 10.86% = 10.86/100 = 0.1086

t = 10

year

Therefore,

A = 13000 x e(0.1086 x 1)

A = 13000 x e(0.1086)

A = $14491.3

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

faster, im not sure why but i know it is faster